AN OPTIMAL SPATIO-TEMPERAL PATH ALGORITHM FOR URBAN EMERGENCY
RESCUE
Min Cai a, *, Yuejin Deng a, Zhongri Tang a
a
Wuhan University, LIESMARS, 430079 Wuhan, Hubei, China –standby211@qq.com, whudyj2010@gmail.com
KEY WORDS: Optimal path, Time influence model, Emergency rescue
ABSTRACT:
As the development of the Geospatial Information System (GIS), the application of GIS has spread a variety of realms such as urban
plan, resource management, transportation, environmental protection, surveying, and mapping. Especially the GIS-based path plan
algorithm is widely applied for the rescue of emergency, such as earthquakes, forest fires, urban accidents, etc. In an emergency
system, there are three essential keys to shorten emergency response time. Firstly, there should get real-time position of patrol cars.
Secondly, it should obtain emergency resources timely. Lastly, there should be a real-time spatial search method which is based
GIS/GPS emergency response system to get the shortest path for best emergency response force. There are many algorithms for
optimal path computing. Most of these algorithms can give the shortest path results. However, since the shortest path is not surely
the best path with least time-consuming, it is necessary to consider some factors such as the number of lanes, traffic volume, road
length, road conditions, driving rules in the optimal path computing. In this paper, we provide an improved quick Dijkstra algorithm
regarding these factors, instead of taking the shortest distance as target function, the least time is primary taken into account and the
time influence model is used in this method. A simulated case study for urban emergency rescue using high-precision geospatial data
and all related information such as lanes, traffic volume, length, conditions, and driving rules shows this approach feasible.
1. INTRODUCTION
Since urban emergency incidents have the characteristics of
unpredictability, continuity, calamity, denseness, diffusivity and
sociability, incidents occurred in different time, places and
immediate environments vary. Besides, the state of the city’s
fire fighting power and the real-time traffic conditions are in a
dynamic changing position. These factors have greatly
increased the difficulty of rescue. Once the rescue is not timely
given, it will bring huge casualties and property losses.
Therefore, an optimal spatio-temperal path algorithm based on
GIS for urban emergency rescue has great significance, which
can be used to assist emergency rescue, reduce losses and
control the disaster.
Many scholars had made researches on the emergency rescue
systems using GIS technology as a tool to the assessment and
rescue of forest fires, urban fires and so on. Tsai Yichang, et al.
(2002) proposed a prototype of real time Emergency Response
System (ERS) based on GIS/GPS. There are three essential keys
in an emergency system to shorten emergency response time.
Firstly, there should get real-time position of patrol cars.
Secondly, it should obtain emergency resources timely. Lastly,
there should be a real-time spatial search method which is based
GIS/GPS emergency response system to get the shortest path for
best emergency response force. Kurt Mehlhorn and Guido
Schaefer (2001) proposed the popular A*Heuristic algorithm
applied in transportation network path optimization. WangJing
Cun, et al. (2007) applied Graph Theory and other related
knowledge to propose the optimal path for emergency rescue
computational modelling based on Floyd Algorithm, which
combined with transportation weighted graph. Skriver AJV and
Andersen KA (2000) applied the Dijkstra shortest path
algorithm to the urban intelligent fire fighting management
system based on GIS. Agustina B. and Coello CA (updated
2010) give a list of more than 4800 references on evolutionary
multi-objective optimization.
At present, the shortest path algorithm mainly includes Floyd
algorithm, Ant Colony algorithm，A* algorithm and Dijkstra
algorithm, etc. (V. Vassilevska, etc., 2006). The Floyd
algorithm and the related extended algorithms were designed to
solve the shortest path between any two vertexes by calculating
the weight matrix of graph. These algorithms’ time complexity
3
is O (n ) , allowing extra edges with negative weight, but not
with negative weight circles. The Ant Colony Algorithm is a
distributed algorithm with adaptive features and a randomly
searching algorithm, which does not require a large number of
probability calculations and the creation of complex
mathematical models, easy to implementation. The A*
algorithm is a multi-source algorithm to calculate the shortest
path between points (J. C. N. Clímaco and M. M. B. Pascoal,
2007). The Dijkstra algorithm is a single-source algorithm,
computing the shortest path from a select point to other points.
In order to guarantee the shortest distance from the starting
point to the current node, the Dijkstra algorithm requires
searching all visited nodes, including the anti-direction
searching. In this paper, the improved Dijkstra algorithm is used
by calculating the sum of the path weight from the starting point
to the current node as the greedy selection strategy.
Network topology structure is the basis for dealing with path
analysis. WangJing Cun, et al. (2007) presented an approach to
the network topology structure’ extraction and building in the
experimental system for shortest path analysis. The A *
Algorithm define data structure for the organization of road
network topology.
* LIESMARS, Wuhan University, 430079 Wuhan, Hubei, China. Email:standby211@qq.com.
A special joint symposium of ISPRS Technical Commission IV & AutoCarto
in conjunction with
ASPRS/CaGIS 2010 Fall Specialty Conference
November 15-19, 2010 Orlando, Florida
Nowadays, with the development of GIS applied in urban
emergency rescue, there still exist some problems in optimal
path planning. Firstly, the majority of the urban emergency
rescue systems based on GIS has implemented the shortest path
planning algorithm, but does not consider how to implement the
shortest path planning in the condition of real-time traffic.
Secondly, there is lack of overall planning for the distributed
rescue power. Thirdly, there are some problems in the
implement of algorithm efficiency. Lastly, there exist some
irrational aspects in comprehensive analysis of the various road
factors affected the rescue time. This paper focuses on the
optimal path planning and algorithm efficiency. Also, we
simulate the actual time consuming in paths by utilizing time
influence model which provides scientific decision–making to
support rapid emergency rescue.
int x;
int y;
int ID;
bool blsOpen;
bool blsClose;
int ParentIndex;
float H;
float G;
float F;
int NeighborCount;
std::vector<int>Neighbor;
2. TIME INFLUENCE MODEL FOR PATH PLANNING
2.1 Urban Emergency Rescue System
The data flow diagram of the urban emergency rescue system is
demonstrated in Figure 1.
Figure 1. Data flow of the urban emergency rescue system
2.2 Toplogical Data Structure for Urban Road Network
Network topology structure describes the network connectivity
relationships of the points, lines and planes. The classic storage
structure for road network topology data mainly includes
adjacency matrix and adjacency list, etc. (X. Gandibleux, F.
Beugnies and S. Randriamasy, 2006). When we use adjacency
matrix to store a large number of road network with sparse
graphs, it would cause great waste of space storage although the
relationship of the nodes’ in-out degree is obvious. Compared
to adjacency matrix, adjacency list significant saves storage
space. At the same time, it requires storing not only the data of
road network of nodes but also the linking information such as
the chain domain data; also the relationship of the in-out degree
is not obvious. Therefore, we define a new topological data
structure for road network data identified with nodes, which
applies to the Dijkstra algorithm. The topological data structure
is shown as follow:
std::vector<float>NeighborDistance;
};
Where x, y is the node coordinate after transformation,
ID
is the node’s ID, blsOpen and blsClose is used to identify the
nodes in the Open table or Close table or neither, ParentIndex is
the current node's parent node index, H, G, F is the variables of
the objective function, F=G+H, NeighborCount is the count of
nodes adjacent to the current node, Neighbor is the index of
nodes adjacent to the current node, NeighborDistance is the
weight corresponding with the Neighbor from the current node
to the adjacent nodes. Neighbordistance stored the same order
as Neighbor.
The representation of the road network means how the road
networks are represented and stored in the computer
(Hershberger, J.,Suri,S, 1999). It is the basis of calculation
method of the optimal path planning. The whole road network
is displayed as a graph that consists of all nodes and arcs.
Therefore, the optimization of topological data structure for
urban road networks has greatly reduced the stored space and
has greater efficiency than the not optimization stored ways,
which helps to significantly reduce the running time, costing
only about 70% of the time of the previous way (Pettie, S.,
Ramachandran, V., and Srinath,S,2002).
2.3 Time Influence Model
According to the knowledge of emergency rescue, we could get
the unreliable search results if we just search the shortest path
by its length. The better realistic path planning could be found
if the number of lanes, traffic volume, road condition and
driving rules and other factors impacting on the actual driving
time are under consideration. According to the thought of
adaptive control and all kinds of factors, it is necessary to model
and analyze of various factors in the optimal path planning. In
our approach, we take the shortest time as the objective function
in the optimal path planning with four factors: number of lanes,
traffic volume, road condition and driving rules.
K  K ( L, N , C, R)  ( K (C )  K ( L)) / ( K ( N )  K ( R))
Where
L represents for the coefficient of the number of lanes,
Struct Node
N
{
from real-time transportation database , C represents for the
is the coefficient of traffic volume obtained and updated
A special joint symposium of ISPRS Technical Commission IV & AutoCarto
in conjunction with
ASPRS/CaGIS 2010 Fall Specialty Conference
November 15-19, 2010 Orlando, Florida
coefficient of road conditions,
R
for the coefficient of driving
rules, and K () for the coefficient of the weight determined by
experts for each factor.
In this time influence model, we should obtain the related realtime information and update the database immediately to extract
the need information, which increased the algorithm’s
complexity in some respects. However, we have established the
adaptive mathematical model to dynamically determine the
weight of each road, and the weight was the essential
information for searching the optimal path. In the next part odf
this paper, we will introduce how to get the different
coefficients in the above model.
2.4 The Number of Lanes
According to urban road design technical standards in china,
roads are classified into four grades, including expressway,
arterial road, secondary road, and branch road. Different grades
correspond to different road capacity (see Table1).
Road grading
Expressway
arterial
Secondary
road
Branch
road
Road
capacity(pcu/h)
1600
1400
800
400
Table 1.Road capacity
So we define the value of the number of lanes as:
K ( L )  grade X road capacity/ branch road capacity.
2.5 Traffic Volume
According to the habits of living and working in china, there are
four traffic peaks every-day. They are two outgoings in the
morning and afternoon and two returns at noon and night. We
define the time it takes as t1, t 2, t 3, t 4 .The percentage of the
traffic is changed into one-way traffic. So we could get the
weight coefficients of road (see Table 2).
One-way or
two-way
One-way
Two-way
Forbidden
Weights
coefficient
0.5
1
∞
Table 2. The weight coefficient of driving rules
2.7 Road Conditions
Different road conditions can impact on the driving, so we must
take the road conditions into considerations. Road friction
coefficients are the friction ability between tire and road; it
relies on the road conditions. The drivers of rescue vehicles
could drive safely according to the road conditions. So the road
friction coefficients could describe quantitatively the road
capacity in order to get the value of weights coefficient. We
could get the formula of the road volume friction coefficient:
 xp  0.92  0.1304e
Where  as the coefficient of characterization of friction
impact factor of the road conditions (see Table 3.),
v
as the coefficient of speed ,

as the coefficient of carload ,
traffic
 xpb
N 2  [(1  n1)  (1  n2)  (1  n3)  (1  n4)] /
(24  t1  t 2  t 3  t 4) is the percentage of which
average
traffic volume each hour during not traffic peak to all-day
volume. So we get:
K ( N ) = N1 / N 2 .
2.6 Driving Rules
Using the Dijkstra algorithm, the shortest path may be
forbidden, because the flow of vehicles goes one way only on
one-way traffic. However, the one-way traffic could increase
traffic capacity under the same road grade. According to traffic
and transportation handbook of the United States, the road
capacity could increase by 20% to 50% when the two-way
as
as the coefficient of the standard volume friction
coefficient when
  0, v  0, FX  0 ,
So we get:
K (C )   XPB /  XP .
is
of the which average traffic volume each hour during traffic
peak to whole-day traffic volume. And the formula
  FX / FY , FX
coefficient of the actual carload of the tire, FY as coefficient of
the standard carload,
n1, n2, n3, n4 and the formula
N 1 =( n1  n2  n3  n4 )÷( t1  t 2  t 3  t 4 ) is the percentage
whole-day

 0.002e (64  v )  0.0426 u
Road
condition

Dry
Wet
Incompact
Compaction
Ice-dry
Puddl
-e
0
0.13
0.6
0.75
1.0
1.2
Table 3. The common value of 
3. THE OPTIMIZATION OF THE DIJKSTRA
ALGORITHM
The Dijkstra algorithm is a classical algorithm for solving the
optimal path. By using the Dijkstra algorithm, we search the
shortest path according to road weights increasing (Wagner, D.,
Willhalm,T., and Zaroliagis, C., 2005). This method is effective
for one-node to all-nodes or all-nodes to one-node. But by
searching the shortest path between two nodes, the method is
2
inefficient and O ( n ) is very high because we have to search
too many unnecessary nodes and lines. So we use the function
A special joint symposium of ISPRS Technical Commission IV & AutoCarto
in conjunction with
ASPRS/CaGIS 2010 Fall Specialty Conference
November 15-19, 2010 Orlando, Florida
to solve the problems mentioned above. The function includes
two parts. One is beeline distance is the shortest between two
points, namely related information, the other is dynamic road
weights (Pinto L, Pascoal M., 2009.). According to the beeline
distance between two nodes is the shortest; the function
limitation strategy is put forward to narrow search area,
reducing the number of search nodes and the time complexity in
order to accelerate the search speed. The path length is defined
to the sum of the weight of all edges. And the specific meaning
of the path length depends on the edges’ weights representing
the significance (Aleksandrov,L., Maheshwari,A., Sack,J.-R.,
2003). In this paper, we set the weight of the edge as the actual
passage of time, where T equalled that the road length (S) was
divided by the result of vehicle limited speed (V) multiplied by
the time influence factors (K). The basic idea of the algorithm is
as follow: set S as the vertex sets with shortest distance having
fixed, named in red vertexes set; set V-S as the vertex sets with
shortest distance not having fixed, named in blue vertexes set.
So the distance is defined as:
Figure2. A searching the optimal path from simulation
Di  ( Xx  Xp)2  (Yx  Yp)2
Where x represents for the temp node, and
node.
5. CONCLUSIONS
p for the target
The process of the algorithm is described below.
(1) Initialization
Only the beginning point S’ shortest distance was already
known: SD (s) equalled zero. So the set of red vertexes S
equalled {s} and the set of blue vertexes was empty.
(2) Calculating each vertex’s shortest path ( Di ) toward the
road length’s increment direction.
(3) Choosing a blue vertex with minimum in the shortest
path from the current set of blue vertexes to expand the red
vertexes set.
(4) Repeating the second step when the blue dots’ shortest
path was remaining endless in the blue vertexes set or all of the
vertexes have expanded to red vertexes set. Finally, the shortest
paths from S to other vertexes have gotten.
4. A CASE STUDY
In this paper, we use the data of road network in Wuhan city
and the data from Emergency Command Centres to simulation
analysis. In this case study, we use ArcSDE to access and
manage the spatial data in Oracle and use ArcObjects to
visualize the planning results as shown in Fig. 2.
This paper proposes a fast algorithm for the optimal path
planning based on GIS. On the basis of UGIS, the optimal
algorithm suppose the shortest time-consumed from the location
of each rescue unit to the location of the incident as an objective
function, designed to provide scientific support for fast urban
emergency rescue.
2
The Dijkstra Algorithm's time complexity is O (n ) .Utilizing
Node-based data structure, there stored the number of nodes
adjacent to the current node, point to identify and the node to
adjacent node weight in the data structure. There introduces the
queue corresponding to the related operations such as insert,
sort , delete, insert and delete, of which time complexity was
O(1) in the optimization of algorithm. However, the time
complexity is O (
) with fast sorting algorithm. Therefore,
the whole algorithm’s time complexity is reduced to O
(n3/2 ) through
these methods. When n is large enough, the
algorithm’s time complexity is greatly lowered.
References
Agustina Buccella, Coello CA, 2010. List of References on
EvolutionaryMulti-objectiveOptimization.
http://www.lania.mx/~ccoello/EMOO/EMOObib.html (accessed
13 Sept., 2010).
Aleksandrov,L., Maheshwari,A., Sack,J.-R., 2003. An Improved
Approximation Algorithm for Computing Geometric Shortest
Paths. In: Proc. of the 14th Internet. Sympos.Fundam.
Computer. Theory (FCT’03).Lecture Notes in Computer
Science, vol. 2751, pp. 246–257.
Hershberger,J.,Suri,S., 1999. An Optimal Algorithm for
Euclidean Shortest Paths in the Plane. SIAMMJ.Computer.28
(6), pp.2215-2256.
J. C. N. Cl´imaco and M. M. B. Pascoal, 2007. “Finding nondominated shortest pairs of disjoint simple paths”, Technical
Report, no. 3,INESC-Coimbra,pp.199-208.
A special joint symposium of ISPRS Technical Commission IV & AutoCarto
in conjunction with
ASPRS/CaGIS 2010 Fall Specialty Conference
November 15-19, 2010 Orlando, Florida
Kurt Mehlhorn, Guido Schaefer, 2001. A Heuristic for Dijkstra
Algorithm with Many Targets and Its Use in Weighted
Matching Algorithms. The 9th Annual European Symposium
on Algorithms - ESA, Arhus, pp.242-253.
Pettie, S., Ramachandran, V., and Srinath,S., 2002.
Experimental Evaluation of a New Shortest Path Algorithm.
UTCS Technical Report TR0137, In Proceedings of the 4th
Workshop on Algorithm Engineering and Experiments
(ALENEX02), Lecture Notes in Computer Science, pp.105-120.
Pinto L, Pascoal M., 2009. Enhanced Algorithms for Tricriteria
Shortest Path Problems with Two Bottleneck Objective
Functions, Technical Report No. 3, INESC-Coimbra, pp.17741779.
Skriver AJV, Andersen KA, 2000. A Label Correcting Approach
for Solving Bicriterin Shortest Path Problems. Technical report,
Department of Operations Research, University of Aarhus,
Denmark. Computers and Operations Research, 27(6), pp. 507524.
V. Vassilevska, R. Williams, and R. Yuster, 2006. Finding the
Smallest H-subgraph in Real Weighted Graphs and Related
Problems. In LNCS ICALP 33rd 4051, pp.262--273.
WangJing Cun,ZhangXiao Tong, 2007. A Heuristic
Optimization Path-finding Algorithm Based on Dijkstra
Algorithm. Journal of University of Science and Technology
Beijing, 29(3), pp.346-350.
Wagner, D., Willhalm,T., and Zaroliagis, C., 2005. Geometric
Containers for Efficient Shortest Path Computation, Journal of
Experimental Algorithmics, 10( 1), pp.15-47.
X. Gandibleux, F. Beugnies and S. Randriamasy, 2006. Multiobjective Shortest Path Problems with a Maxmin Cost Function,
4OR – Quarterly Journal of the Belgian, French and Italian
Operations Research Societies (4), pp. 47–59.
Yichang (James) Tsai, Zhaohua Wang, and Chien-Tai Yang,
2002. A Prototype Real-Time GPS/GIS-Based Emergency
Response System for Locating and Dispatching Moving Patrol
Vehicles with the Beat-Based Shortest Distance Search.
Proceedings of the Third International Conference on Traffic
and Transportation Studies, pp. 669-678.
Acknowledgements
This paper is supported by the project named Optimal Path
Planning Algorithm for Urban Emergency System Based on
GIS, which was sponsored by the Chinese Academy of
Surveying and Mapping (Project No. 2009-04). The authors
also appreciate the softwares from Wuda Geoinformatics Co.,
Ltd. in our experiment.
A special joint symposium of ISPRS Technical Commission IV & AutoCarto
in conjunction with
ASPRS/CaGIS 2010 Fall Specialty Conference
November 15-19, 2010 Orlando, Florida